Evaluate: `int1/(sinxcos^3x)\ dx`

Explanation

`int frac{d x}{sin x cdot cos ^{3} x}`


Dividing numerator and denominaor by `cos ^{4} x`

`=int frac{frac{1}{cos ^{4} x} d x}{frac{sin x cdot cos ^{3} x}{cos ^{4} x}} int frac{cdot sec ^{4} x d x}{tan x} int frac{sec ^{2} x cdot sec ^{2} x d x}{tan x} =int frac{(1+tan ^{2} x) cdot sec ^{2} x}{tan x} d x `

Let `tan x=t`

`Rightarrow sec ^{2} x=frac{d x}{d t}`


`Rightarrow sec ^{2} x d x=d t`

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